在這個計劃中，我們會對黑洞物理的幾個課題進行研究。首先，是高 維黑洞方面，我們會考慮一般旋轉黑洞的純量和費米子的準正常態，以及 Hawking 放射的機率。接著我們會利用Killing 張量的方法，加上Hertz 勢 的應用，來探討其他自旋微擾方程式，從而分析高維黑洞的穩定性和 Hawking 輻射。下一個課題是運用stochastic 重力理論，來研究在anti-de Sitter 和de Sitter 時空中，量子場的演變，並藉此了解dS 事件視界的量子波動。 另外，我們也會進一步探討一般黑洞和AdS 黑洞的量子演變。最後，我們 希望考慮在早期暴脹宇宙的dS 時空中，各種如黑洞的微擾，對於不同的量 子場的影響。並藉此探討其在宇宙背景輻射所留下的痕跡，以及與早期磁 場產生機制的關係。 In this proposal we plan to study some topics related to the physics of black holes. First, on the higher-dimensional black holes, we shall consider the scalar and the fermionic quasinormal modes of rotating black holes with more than one rotations. Then using the methods of Killing tensors and of the Hertz potential, we shall investigate the higher spin perturbation equations of these black holes. After separating these equations, we could analyze their stability and also the Hawking radiation related to their decays. The next topic is on the theory of stochastic gravity. We shall study the evolutions of quantum fields in anti-de Sitter and de Sitter spacetimes and to understand the effects of quantum fluctuations on the de Sitter horizon. Afterwards we shall consider the fluctuations of quantum fields in AdS black holes spacetimes. Lastly, we shall study the effects of spacetime perturbations on the fluctuations of quantum fields in de Sitter spacetime which describes the early inflationary universe. We shall consider the situations with different spin fields and use the result to investigate their effects on the cosmic microwave background and also on the production of primordial magnetic fields.
